Newton's Laws

Introduction

Join High School physics teacher Don Rathjen and Professor Paul Doherty to do some activities exploring Newton's Laws of motion.

1. Objects at rest remain at rest, objects in motion remain in motion is a straight line at a constant speed unless acted upon by a net force.
2. F = ma
3. For every action there is an equal and opposite reaction.

Newton's First Law.

Take a massive object like a bowling ball, place it on the floor. Notice that it does not move. You are experiencing the first half of Newton's first law.

In fact, anytime you see someone just sitting there doing nothing you can turn to a fellow scientist and say, "They sure are an excellent example of the first half of Newton's first law, aren't they?"

To really see how an object in motion remains in motion you need to eliminate all net forces such as the effects of friction. You can do this by building a frictionless air puck.

Frictionless Airpuck A frictionless air puck made from a compact disk and a balloon.

There are also plans available in the Physics teacher magazine on how to build a frictionless airpuck that a person can ride.

If you have a smooth level table and give the airpuck a push it will continue across the table in a straight line at a constant velocity.

If the air puck changes speed or makes a curve then you know that there are net forces on it.

An object experiences a net force when the sum of the forces on it is not zero.
Stand still on the floor and the net force on you is zero.
There is a large gravitational force on you downward plus an equally large contact force from the floor upward. These two forces sum to zero.

2. Newton's Second Law: F = ma

Mass is not force.

This is one place where physicists take common words and give them different scientific meaning.

Mass is measured in kilograms.

Force is measured in newtons.

Newton's second law tells how much force, F, is needed to accelerate with acceleration, a, a mass m.

A 1 newton force will accelerate 0.1 kilograms with an acceleration of 10 meters per second squared.

Don points out that 10 meters per second squared is 10 meters per second per second.

Remember that 10 meters per second is a speed. (about 20 miles per hour.)

So an object that starts out at rest and accelerates at 10 meters per second squared is going 10 meters per second or 20 miles per hour after one second.

It is going 20 meters per second or 40 miles per hour after 2 seconds.

And, it is going 30 meters per second or 60 mph after 3 seconds.

Now, I chose 10 meters per second as an acceleration for a reason. If you drop something near the surface of the earth it will accelerate at nearly 10 m/s2 (actually 9.8 m/s2.)

So the acceleration of gravity which is usually given the symbol, g, is 10 m/s2. If a car drives off a cliff it will accelerate 0 to 60 mph in 3 seconds.

Top Fuel dragsters accelerate at 4 times the acceleration of gravity, we say they accelerate at 4 g's. They go 0 to 60 mph in under 1 second.

the weight of an object is the force needed to support it against gravity. Experiments show that near the surface of the earth the weight, W, of an object of mass, m, is W= mg.

Use Newton's Laws to find the acceleration of an object of weight W and find that

a = F/m

a = W/m

a = mg/m

a = g

Paul Notes that in the British system of units an object that weighs 1/4 pound has a 1 Newton force on it. Thus, in the metric system, a McDonalds quarter pounder is a Newton Burger.

Don notes that many D cell batteries weigh 100 grams, or 0.1 kilogram. so the weight of these batteries is 1 Newton.

To demonstrate the different accelerations produced when the same force is applied to two objects with different masses, I attached a spring scale which could exert 20 Newton's to myself. I have a mass of 70 kg, I use myself as the mass to avoid embarrassing students who might be sensitive about their weight. I sat on a skateboard (or a frictionless airpuck) and had a student pull on me so the scale read 10 Newtons. We observed my acceleration. (a = F/m = 10N /70 kg = 1/7 m/s2)

Then I had the students pull on me with a force of 20 N.

My acceleration was then double, a = 20N/70 kg = 2/7 m/s2.

If you have a less massive person who is willing to let their mass in kilograms be known to the entire class you can use them and measure their accelerations under applied forces of 10 N and 20 N.

3. Newton's Third Law: Action-Reaction

Don Rathjen's important note:

Action and Reaction forces can always be separated into forces on two different objects.

By using two spring scales you can do some experiments on action and reaction.

Consider a tug of war.

Two people at opposite ends of a rope pull on each other trying to make the other person move across a line.

Here is a question that is purposefully stated in a misleading way.

Since the force that person 1 exerts on person 2 is equal and opposite to the reaction force that person 2 exerts on person 1, how can anyone ever win a tug of war?

To answer this question consider the forces on one person only.

This is an important general rule: First, before starting any problem about motion, always draw a border around the object whose motion you want to study. You must identify an object before proceeding.

Then draw all of the forces on that object.

In the case of the tug of war one choice is one of the people.

The forces on that person are:

• The force of gravity down,
• The force of the ground up (these two forces are equal and opposite but they are not an action reaction pair because they are on the same object.)
• The upward contact force of the rope on person 1
• The friction force of the ground on person 1.

If the force of the rope exceeds the friction force exerted by the ground then this person will accelerate toward the rope and perhaps lose the tug of war.

Another choice for the tug of war is to draw both persons and the rope as the object within the boundary. You can ignore the forces that are purely within the boundary, the forces on on the rope and by the rope on the people can thus be ignored.

The acceleration of people and rope comes about due to the forces on the system:

Gravity down, contact forces up, friction forces on one set of people, friction forces on the other set of people. If the friction forces of the ground on one set of people is not equal and opposite to the friction forces on the other set, then the object will accelerate and one group will win.

 Scientific Explorations with Paul Doherty © 2001 26 April 2001